Do Firm-Level Shocks Generate Aggregate Fluctuations?

Transcription

1 Do Firm-Level Shocks Generate Aggregate Fluctuations? Shuheng Lin Boston University Maria Francisca Perez Boston University July 04 Abstract This paper empirically examines the contribution of firm-level idiosyncratic shocks to aggregate fluctuations in the US, Germany, Canada, and the UK. We find shocks to large firms are of little relevance in the UK or Canada, but roughly explain one third of output fluctuations in the US and Germany. We argue the ability of the largest firms to transmit shocks is not universal, even when the firm size distribution is highly skewed as the theory suggests. Keywords: Aggregate Shocks, Idiosyncratic Shocks, Firm Size Distribution, Total Factor Productivity We thank Stefania Garetto, Alisdair McKay, Simon Gilchrist and Anindya Chakrabarti for extremely helpful comments. We also benefited from discussions with particiants at the Macroeconomics Dissertation Workshop in Boston University and with Xavier Gabaix over s. All errors are ours.

2 Introduction Business cycle fluctuations are often thought to have caused by aggregate shocks, since uncorrelated sector- or firm-level shocks average out in the aggregate due to the law of large numbers. However, a number of studies in recent years show the diversification of idiosyncratic shocks breaks down when sectoral linkages or firm size distributions are highly skewed. These studies provide the insight that in an economy where few sectors serve as major input suppliers or few firms account for a disproportionate share of production, shocks to these sectors or firms can propagate to generate aggregate fluctuations. While the sector-based story has a long theoretical tradition accompanied by empirical evidence, the relevance of firm-level shocks to aggregate fluctuations remains to be acknowledged and quantified. Gabaix (0) was the first study to formally show that in an economy with fat-tailed size distribution of firms, idiosyncratic shocks to firms diversify at a milder rate that leads to nontrivial effects on aggregate fluctuations. Further, output volatility originated from micro-shocks is an increasing function of the Herfindahl index of firms sales shares, or in other words, of how concentrated the economy is. The theoretical framework is then accompanied by an empirical analysis where the author shows shocks to largest firms in the US statistically explains GDP growth over the period In light of Gabaix s theory, countries that are more concentrated than the US should observe stronger effects of firm-level shocks on aggregate fluctuations. However, since the theory is relatively new and comprehensive panel data are not readily available for many countries, studies investigating the effects of idiosyncratic shocks outside the US are scarce. This paper contributes to the existing literature by examining the relevance of idiosyncratic shocks to output fluctuations for three OECD countries (Germany, Canada and the UK) in addition to the US. Figure a presents the relative size of the top 00 firms in terms of their Sector-based stories date back to the seminal work of Long and Plosser (98) where they show input-output linkages can propagate independent production shocks in each sector over time and across sectors with a sixsector dynamic stochastic general equilibrium model. This study was later challenged by Dupor (999) because if the number of sectors is large enough, positive shocks in one sector can still be neutralized by negative shocks in others. Though around the same time Horvath (998, 000) argue the cancellation of sector-specific shocks is affected by the existence of factor demand linkages; whether shocks diversify depends on not the number of sectors but whether there are a handful of them that are important inputs in the production processes of many others. Two recent studies, Carvalho (008); Acemoglu, Carvalho, Ozdaglar, and Tahbaz Salehi (0), build on Horvath s insight and show that if there are only few input supplier sectors then the convergence of aggregate volatility to zero slows down considerably. A productivity shock in one major sector has a cascading effects in the economy and as a result affects not only the direct downstream sectors but also the series of them that are interconnected with each other. In all aforementioned studies, the authors provide also empirical exercises that support their theoretical models. The results in Gabaix (0) only require economies with sufficiently large herfindahls. The central case of firms size being Zipf-distributed is justified because of its tractability and clean exposition. distribution generates very high herfindahls. Also, this

3 sales to GDP ratio in these four economies, and Figure b the Herfindahl index of firms sales share among the largest 00 firms. Comparing with the US, the top 00 firms in other countries not only account for a larger share of their corresponding GDP, they are also much more concentrated. These descriptive statistics suggest large firms in these countries could be an important source of variability, and the effects of idiosyncratic shocks on the aggregate should be stronger as a result. To assess the empirical relevance of idiosyncratic shocks for output fluctuations in these countries, we regress the growth of GDP per capita on the granular residual and its different lags. The granular residual, proposed by Gabaix (0), is a transparent statistic that summarizes the importance of firm idiosyncratic shocks using the weighted sum of firm-level shocks, where the weights are calculated as the firms sales to GDP ratio to reflect their relative importance. This empirical strategy allows us to work with a broader sample of countries as we do not require input-output matrices to measure the importance of firm-level productivity shocks for the economy, only annual firms sales and employment, and countries GDP per capita are necessary. Figure : Relative Size and Degree of Concentration of Top 00 Firms by Country Sum of Sales/GDP Year US Germany UK Canada Herfindahl Year US Germany UK Canada Herfindahl index for firms that make it to the top 00. (a) Top 00 Firms Sales to GDP Ratio (b) Herfindahl index of top 00 firms Our results show that idiosyncratic shocks to large firms are of little relevance in the UK or Canada but explain roughly / of the output fluctuations in the US and Germany. Further investigation indicates the top ranking firms are indeed the most important contributors to granular effects, but because diversification is at work still in the UK and Canada these firms are not able to explain GDP growth. Our study suggests that while firm size distribution is found to be highly skewed in many economies 4, the ability of the largest firms to transmit Despite using an empirical strategy that is lenient on data requirements, we still face some data limitations along the time-series dimension. In the end, we are able to construct the granular residual using the top 00 firms for at least 0 years for all of our countries. 4 di Giovanni and Levchenko (0) find in a set of 4 countries, firm size distributions are highly skewed

4 shocks may not be universal and thus not to be taken for granted. The studies closest to ours are di Giovanni, Levchenko, and Méjean (04) and Foerster, Sarte, and Watson (0); both studies investigate the importance of firm level shocks, but they focus on one country each and differ in methodology. While the first finds support for the hypothesis that microeconomic shocks drive aggregate fluctuations, like ours the second paper casts doubts on the validity of this hypothesis. Using detailed French firm level data, di Giovanni et al. (04) find firm-specific shocks to be almost twice as important as the combined effect of sectoral and macroeconomics shocks in driving aggregate sales growth. Further, they find that most of the effect is not coming directly from shocks to individual firms, but input-output linkages. Foerster et al. (0) uses factor methods to decompose US industrial production and explore the plausibility of the granular- and network-origins hypothesis of aggregate fluctuations. They find no support for the granular hypothesis, and aggregate volatility is better explained by co-variability among sectors. Furthermore, covariability is explained by common factors, very little of which is the result of the transmission via input-output linkages. The rest of the paper is organized as follows. Section describes the empirical specification used to estimate the importance of firm-level idiosyncratic shocks. In Section we present the regression results for the countries in our sample, and in Section 4 we deconstruct the differences in the findings for the US and Germany versus those for the UK and Canada. Finally our conclusions are summarized in Section 5. Empirical Strategy In this section, we first summarize the theoretical framework from which the granular residual is derived and how to construct it. We then specify the empirical strategy and describe the data.. Granular residual In an economy with input-output linkages and endogenous input response, aggregate productivity growth is a weighted sum of firms Hicks-neutral productivity growth, g zi : g T F P = i sales of firm i g zi, () GDP sales of firm i GDP where the weights i capture the propagation effect from firm-level shocks to the rest of the economy. Domar (96) and Hulten (978) show that these are the appropriate weights to measure the total effect of firm-level productivity changes on aggregate productivity. and on average close to Zipf. 4

5 The intuition is that an increase in productivity in firm i will increase output of other firms that use firm i s good as an intermediate input, which in turn increases output again, and so on. Without disturbances, growth in GDP is proportional to the growth in TFP: g GDP = µ g T F P, () where µ is the factor usage intensity that is a combination of the elasticity of substitution of labor and output elasticities with respect to production inputs. 5 Combining () and (), the impact of idiosyncratic shocks on aggregate output is captured by the following relationship: g GDP = µ i sales of firm i g zi, () GDP where Γ = sales of firm i i GDP g zi is Gabaix s granular residual. Equation () provides the basis for the regression framework to test the granular hypothesis: granular effects are said to be present when the weighted sum of idiosyncratic shocks to large firms statistically explains GDP fluctuations as measured by growth in GDP per capita. The only detailed calculation of this empirical strategy is the construction of firm level shocks. To avoid data availability issues, we also estimate firm-level productivity using labor productivity of firm i: 6 z i = ln sales of firm i in year t number of employees in firm i in year t. (4) To compute the shocks to firms productivity growth, we model firms labor productivity growth, g, as depending on a set of firm s characteristics, X ijt, and an idiosyncratic shock, ε ijt : g ijt = β X ijt + ε ijt. (5) For simplicity, we use year and industry dummies to proxy for firm s characteristics: g it = c + d t + ε it (6) g ijt = c + d t + IND jt + ε ijt, (7) 5 Consider an economy with the production technology Y = A tl α t and consumer preference U t(c t, L t) = log(c t L+/φ t +/φ (αa t) +/φ α ). With competitive markets for output and labor, the equilibrium is characterized by Nt = and Y t = αa +/φ +/φ +/φ α t. In this economy, output growth is proportional to TFP growth Ŷ = µâ, where µ = is the factor usage. 6 +/φ α We implement the Olley and Pakes (996) method to estimate the firm-level Solow residual and contrast it with our measure of labor productivity. We find that the two methods yield similar and highly correlated estimates for the productivity growth in the US. 5

6 and calculate firm level shocks as the demeaned labor productivity growth rates, where the mean is computed over all firms of the year (the case when we use only year dummies), or of the year and industry (when both year and industry dummies are used in the regressions). 7 Using both estimations for the idiosyncratic shocks, we construct two versions of the granular residual : Γ t,v = K=00 i= K=00 S i,t S i,t ˆε it ; Γ t,v = ˆε ijt. (8) Y t Y i= t Since we are interested in the effect of the largest firm we only work with the largest top K = 00 firms ranked by their sales to output ratio in the previous period. 8. Econometric specification To test for the effect of firm-level idiosyncratic shocks on aggregate fluctuations we regress our measure of idiosyncratic shocks, Γ, on growth of GDP per capita using the following specification: g Yt = α + µ i Γ t i + u t. (9) i=0 The R-squared from regressing GDP growth g Yt on Γ t and its different lags allows one to assess the extent to which idiosyncratic shocks explain the variability of GDP growth. If we recall equation (), the coefficient on the granular residual will provide an estimation of the factor usage in these different countries. 9 Table provides a summary of country characteristics in terms of the variables used in the regression model. The average and the volatility of per capita GDP growth across the 7 The challenge with correctly identifying ε it remains apparent as in the data it is hard to identify ε it because aggregate shocks could cause firm i s volatility or reflect it. We do not directly address the reflection problem but we perform robustness checks to also control for the common factors so to prove the explanatory power of the granular residual is not coming from aggregate shocks (e.g. oil, monetary, fiscal policy shocks and etc). The reflection problem is studied in (Manski, 007). It is similar to the problem of interpreting the almost simultaneous movements of a person and his reflection in a mirror. Manski points out unless one knows about optics and human behavior, he would not be able to tell whether the mirror image cause the person s movements or reflect them. We attempted to apply the few solution methods that have been proposed in the literature but to no avail. The reason is these solutions all involve exogenous variation that is hard to find in our context. 8 To verify the empirical methodology we simulated a simple economy, with exogenous production and without linkages. With the true idiosyncratic shocks, we constructed the granular residual and regressed output on this measure. The empirical strategy tends to bias the granular residual downwards in its magnitude and volatility, decreasing its explanatory power. Further, it seems to capture well the idiosyncratic components of a firm s productivity growth in a granular world without inducing any spurious bias. Interestingly, the results also show that the explanatory power of the model decreases when the idiosyncratic shocks to large firms are less volatile. 9 Gabaix (0) takes µ =.6 as the benchmark to compare the regression coefficient with for the US. 6

7 countries are very similar (columns and ), but firm-level productivity growth is much more volatile in non-us countries (column 4). Column 5 shows the correlation between growth rates across firms is small for all of the countries, suggesting the measure we use for firm level shock does capture idiosyncratic variation to the firms. Finally, the average and standard deviation of the granular residual are smaller for version than for (columns 6 and 7 for version and 8 and 9 for version ). This shows when we demean by year-industry, we further get rid of industry-specific shocks that could confound our results. Table : Country characteristics () () () (4) (5) (6) (7) (8) (9) µ gy σ gy µ g σ g ρ gi,g j µ Γv σ Γv µ Γv σ Γv US Canada Germany UK µ gy is the average annual per capita GDP growth; σ gy is the standard deviation of annual per capita GDP growth; µ g is the average annual firm-level productivity growth; σ g is the standard deviation of annual firm-level productivity growth; ρ gi,g j is the average annual sample correlation of firmlevel productivity growth; µ Γ is the average annual granular residual with year-demeaning; σ Γ is the standard deviation of the annual granular residual; µ Γ sic is the standard deviation of the annual granular residual with industry demeaning; σ Γ sic is the standard deviation of annual granular residual with industry demeaning.. Data Firm-level data for the US and Canada, UK and Germany are from Compustat North America, Computstat Global. The length of coverage varies and it spans from 950 to present and from 987 to present for NA and international companies. We keep only firms incorporated and headquartered in their home country so to exclude foreign firms to the best of our ability. The oil industry is excluded due to difficulty in teasing out real firm-level shocks from the aggregate commodity price shocks. 0 Figure A. summarizes the number of firms, with valid data required by our regression specification, by country and year for each country. The advantage of using Compustat is the comparability of information reported across countries, but the coverage on the number of firms is limited in Germany and Canada for some of the years. Further, since the analysis is done over the top 00 firms in the economy 0 We also exclude financial firms as in Gabaix (0), because the nature of their sales are not in line with the meaning of gross output in the paper. 7

8 we lose additional observations because for some years there are less than 00 firms. However, since sales of the top 50 and 00 firms as a percentage of GDP track each other closely for Germany and Canada, we restrict our samples to years with at least 50 rather than 00 firms. This means for years less than 00 (but more than 50) firms we use all firms in our empirical exercises. Macroeconomic data (GDP, GDP per capita and GDP deflators) are taken from the World Bank s Development Indicators database. GDP deflators are used to convert sales into real terms. Some of the sales figures in Compustat are denominated in non-local currencies, and we look to the respective country s central bank website to obtain the exchange rates. Estimation Results In this section, we present the estimation results for the US and Canada, UK and Germany as specified in regression (9) for different lags for the granular residual.. Impact of idiosyncratic firm-level shocks Table presents the regression results for the US, Germany, the UK and Canada. Taking the US as the benchmark, we see in columns () & () of Panel A that the granular residual explains 4% (5%) of the fluctuations in GDP growth using () lag(s) when demeaning by year. When we control for the contemporaneous granular residual and its two lags, their coefficients are significant and hovering around.6 the theoretical value of µ Gabaix (0) uses for comparison. The presence of granular effects is confirmed in these results. When we control for industry-year specific shocks by demeaning at the -digit industry level, we observe an increase in the granular effects for the US in Panel B columns () & () of the same table. The resulting firm idiosyncratic shocks are closer to the true ε it when industry specific shocks are controlled for, hence if the granular hypothesis holds we should expect to explain more of GDP fluctuations. The results for the other countries are mixed. For Germany, we find the GR to explain GDP fluctuations even better than for the US (5% (6%) when demeaning by year, and Ideally one would like to use industry production indexes but they are not readily available so we use GDP deflators instead. This could introduce potential measurement errors since the exchange rates were matched to the fiscal years, rather than the period covered by a firm s financial statements. We also experimented with demeaning at the -digit and 4-digit level but the granular effects are weakened as a result. Increasing the level of disaggregation should improve the explanatory power further theoretically but at the same time inducing attenuation bias empirically because the mean would then be estimated with fewer firms. These two forces work against each other and complicate the interpretations of the regression results, hence we focus on year and year-industry at the -digit level demeaning in this paper as mentioned in the Introduction. 8

9 Table : Explanatory power of the granular residual Panel A: GR with year demeaning () () () (4) (5) (6) (7) (8) USA Germany UK Canada Γ t (0.69) (0.69) (0.4) (0.44) (0.) (0.5) (0.58) (0.60) Γ t (0.7) (0.67) (0.4) (0.4) (0.) (0.4) (0.58) (0.59) Γ t (0.7) (0.44) (0.4) (0.59) Intercept (0.00) (0.00) (0.00) (0.00) (0.00) (0.0) (0.00) (0.00) N R adj. R Panel B: GR with -digit industry demeaning () () () (4) (5) (6) (7) (8) USA Germany UK Canada Γ t (0.76) (0.78) (0.6) (0.55) (0.6) (0.68) (0.70) (0.7) Γ t (0.74) (0.7) (0.60) (0.58) (0.59) (0.64) (0.70) (0.70) Γ t (0.75) (0.55) (0.6) (0.70) Intercept (0.00) (0.00) (0.00) (0.00) (0.00) (0.0) (0.00) (0.00) N R adj. R * for p<., ** for p<.05, and *** for p<.0. Standard errors in parenthesis. Depvar: Per capita GDP growth is regressed on the granular residuals calculated over the top 00 firms. 9

10 4% (4%) when demeaning by year-industry). However, regardless of demeaning the GR by year or industry, we do not find granular effects in Canada or the UK. The adjusted R is essentially zero and the coefficients are insignificant and often negative. Even though all countries meet the sufficient conditions, we find idiosyncratic shocks translate to aggregate fluctuations only in the US and Germany. The natural progression at this point is to implement factor methods to examine whether any residual common shocks give rise to our findings, and to use principal component analysis to investigate which firms explain the aggregate fluctuations the most. However, since the identities of the largest firms change from year to year, we cannot use conventional methods to examine whether our findings are driven by common factors or specific firms. Thus in the next section we deconstruct our findings utilizing still the granular residual measure demeaned at the industry level, since this level of demeaning yields the most robust proxy for idiosyncratic shock as shown in Table. 4 Deconstructing the empirical results We first examine the relative importance of top ranking firms amongst themselves in explaining GDP fluctuations. Since the ranking of these top firms changes every year, we drop observations that have the same ranking to construct the new GR. The results are presented in Figure where we drop a top ranked composite firm one at a time and plot the percentage reduction in adjusted-r s against its average weights over the sample period. The figure shows lower ranks bunched together around zero in all four countries, suggesting their relative importance is small. However, the impact of the largest firms is prominent in all countries with the starkest contrast in the case of the US. In light of this finding, we construct the granular residual with just the top 0 ranks to find that the positive findings in the US and Germany can be explained just as well (see Table ). Table 4 additionally shows dropping top 0 ranks reduces the explanatory power significantly and the coefficients are no long significant. In the UK and Canada, however, firms of the same ranks did not play a significant role and dropping them leaves the R as low as before and the coefficients remain insignificant. 4 Since summing up the granular residuals for the top ranks dilute their explanatory power in the UK and Canada, we suspect the diversification mechanism may be at work still in these two countries. To further examine where the differences in the contribution of top firms with comparable importance could be coming from, we construct the rank specific weighted idiosyncratic shock and plot its correlation with GDP growth in Figure. 5 The right column of the figure shows 4 This conclusion is robust to dropping the top 5 ranks. 5 We compute the correlation between GDP growth and the contemporaneous rank-specific GR, with its one lag and then two lags. In the end we plot the average of the three correlations against the rank s average sales 0

11 Figure : Reduction in adjusted-r after Dropping Top Ranked Firms % reduction in adjusted R CAN DEU GBR USA average sales/gdp ratio % reduction relative to the initial R 4 Table : Explanatory power of the granular residual with the top 0 ranks () () () (4) (5) (6) (7) (8) USA Germany UK Canada Γ t (0.74) (0.74) (0.67) (0.6) (0.90) (0.9) (0.69) (0.7) Γ t (0.7) (0.70) (0.66) (0.64) (0.88) (0.9) (0.69) (0.70) Γ t (0.7) (0.6) (0.88) (0.70) Intercept (0.00) (0.00) (0.00) (0.00) (0.0) (0.0) (0.00) (0.00) N R adj. R * p<., ** p<.05, and *** p<.0. Per capita GDP growth is regressed on the granular residuals calculated over the top 0 ranks.

12 Table 4: Explanatory power of the granular residual without the top 0 ranks () () () (4) (5) (6) (7) (8) USA Germany UK Canada Γ t (.50) (.5) (.0) (.09) (.) (.58) (.) (.4) Γ t (.49) (.56) (.) (.54) (.) (.5) (.) (.4) Γ t (.54) (.09) (.6) (.) Intercept (0.00) (0.00) (0.0) (0.0) (0.00) (0.0) (0.00) (0.00) N R adj. R * p<., ** p<.05, and *** p<.0. Per capita GDP growth is regressed on the granular residuals calculated over the top 9-00 firms. unambiguously that the top ranks in Germany and the US are also positively correlated with GDP growth, but the picture is much more nuanced for Canada and the UK. We conclude that the higher tendency of high ranking firms moving in opposite directions in the UK and Canada neutralizes the effect of idiosyncratic shocks, thus it is not surprising the final measure of granular residual the sum do not explain aggregate fluctuations for these two countries. The last piece of the puzzle remains as to why shocks diversify away in the case of the UK and Canada but not in the US or Germany. The reason may be that top ranked firms in these two countries are spread out across more sectors or they are from sectors not as interconnected with the rest of the economy. With our data and methodology we are only able to investigate first possibility here. To do this, we show in Table 5 the distributions of top firms by sectors in 00 and find that they are similar across countries. Thus the positive results in the US and Germany is not purely driven by the fact that top ranking firms are from sectors that are also of disproportionate importance in the economy. to GDP ratio.

13 Table 5: Top 0 sectors in 00 Canada Germany S S Rank SIC # Top Firms Y SIC # Top Firms Y Elec Trans.Eq Food Strs Conglmrts. 7.5 Comm Chem Trans.Eq Comm Metal Ind G.Mechdis.Strs.59 6 G.Mechdis.Strs..8 Metal Ind Chem. 5.6 Trans.Svcs.8 8 Paper and Allied Machne.Eq Lumber Motr.Warehsing Railroad Trans Whsl Tr. 4.0 UK US S S Rank SIC # Top Firms Y SIC # Top Firms Y Food Prd Trans.Eq Chem G.Mechdis.Strs Comm Comm Food Strs Chem G.Mechdis.Strs 4.5 Food Strs MetalMining.0 Conglmrts..6 7 Trans.Eq. 4.8 Food Prd Biz.Svcs Machne.Eq Whsl Tr..5 Biz.Svcs Prntn.Pub Whsl Tr. 4.4 Top 0 sectors as ranked by sector sales of top 00 firms (in the overall economy) in 00.

14 Figure : Correlation between Firm Specific GR and GDP Growth average correlation at SIC level Canada UK USA Germany avergae sales/gdp ratio 4 5 Conclusion This paper quantifies the importance of firm-level idiosyncratic shocks in explaining aggregate fluctuations. It is motivated by the theoretical framework (Gabaix, 0) that shows in an economy with fat-tailed size distribution of firms, law of large numbers breaks down and idiosyncratic shocks to firms diversify at a much milder rate and lead to nontrivial effects on aggregate fluctuations. In the data, firm level shocks are estimated as the demeaned productivity growth rates, where the mean is calculated over top firms of the year or of the year and industry. These shocks are then weighted by firms sales to GDP ratio, and the empirical strategy tests whether the sum of these weighted shocks statistically explains GDP fluctuations. We find shocks to large firms are of little relevance in the UK or Canada but explain roughly / of the output fluctuations in the US and Germany. While top ranking firms contribute the most to granular effects, they do not always sum up to play a significant role in every country. We conclude that the reason they did not explain GDP growth in the UK and Canada is because diversification is at work still in these two countries. Our results suggest while firm size distribution is found to be highly skewed in most economies, the ability of the largest firms to transmit shocks is not universal. Future studies on the micro-foundation of aggregate fluctuations should take into account that apart from the granular theory, other transmission mechanisms may be at work, and the importance of which may differ on a country-by-country basis. 4

15 A Additional figures Figure A.: Number of Firms with Valid Sales and Employee Data Number fo Firms, US Number fo Firms, Non US Year US Germany UK Canada Number of firms with valid sales and employee data, excluding oil and financial industries. 5

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